Despite its tremendous success, earlier particle physics realizations
of WI were confronted with two important difficulties. The first one
was that achieving a thermal radiation bath during inflation can
result in potentially large thermal corrections to the inflaton's
potential, thus, hindering the slow-roll dynamics. Earlier WI model
building constructions circumventing this problem made use of models
with large field
multiplicities [1]}, [2]}, [3]}, [4]},
making them technically unappealing. This issue was later resolved
with the introduction of a new class of WI model building realization
able to sustain a nearly-thermal bath, yet with a small number of
field species [5]}. These type of models were
dubbed “warm little inflaton (WLI)" models. The second difficulty was
that the backreaction of the thermal radiation bath on the inflaton
power spectrum due to a temperature dependent dissipation coefficient
leads to the appearance of growing/decreasing modes in the scalar of
curvature power spectrum [6]}. As a consequence of
this, consistency with the observations could only be achieved in weak
dissipation regimes of WI, thus preventing WI from going into a strong
dissipation regime. However, the strong dissipation regime of WI is
particularly appealing from both a theoretical and effective field
theory point of view. In particular, the strong dissipation regime of
WI can naturally result in a smaller energy scale inflation with
sub-Planckian field excursions. These are features that have been
attracting considerable attention, in special more recently, e.g.,
based on the swampland program aiming at finding effective field
theories which can consistently be embedded in string theory and the
role played by WI in achieving this
goal [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. This
issue was also partially addressed recently by building two distinct
explicit WI models, namely the “variant of warm little inflaton"
(VWLI) [15]} and the “minimal warm inflation"
(MWI) [16]}, [17]}, utilizing different
field contents in each construction. In the VWLI, the strong
dissipative regime is obtained by interpolating between decreasing and
growing modes, while in the MWI it is achievable only for some
particular form of potentials, while growing/decreasing modes for the
power spectrum can still exist in both cases.
